Document Type


Date of Award



College of Science, Engineering, and Technology (COSET)

Degree Name

MS in Mathematics

First Advisor

Professor Robert Nehs


The only nontrivial automorphism of Q and R is the identity function. The rest of the paper is devoted to the study of automorphisms on C. If X is any set of complex numbers which is algebraically independent over Q, then any one-to-one correspondence a:X􁪽X extends to an automorphism F:Q(X)􁪽Q(X) where F(r) = r for rEQ and F(s) = a(s) for SEX. A maximal algebraically independent set in Cover Q is called a transcendence basis of Cover Q. Such a transcendence basis exists and is infinite. It is proved that any automorphism F:Q(X)􁪽Q(X) can be extended to an automorphism on C. This proves there are infinitely many automorphisms on C.